I took the idea of this hypothesis from that by which Don V. V. Queipo inferred the Beládi cubit to be the double measure of the side of a cubical vessel containing a Ptolemaïc talent of water. Certainly it solves the question of the origin of our foot, and it happens that, applied to the equally obscure origin of the Rhineland foot, the results are equally satisfactory. 2. THE RHINELAND FOOT Let the same process of involution be applied to the side of a cubical vessel containing 1000 Troy ounces of water. The standard of Troy weight varied very much, from the Danish value of a little over 481 grains in the ounce, to the French Troy value of 472·13 grains. The Scots Troy weight, = 476·09 grains to the ounce, is nearly the same as the Amsterdam weight, = 476·68 grains. These Troy weights may be taken at three main standards, high, medium, and low, represented by: English Troy, its ounce = 480 grains Amsterdam „ „ „ = 476·68 „ French „ „ „ = 472·13 „ Let us apply to 1000 ounces of water, at the medium Amsterdam standard, = 10 Egyptian dirhems of 47·6 grains, the same measurement of a quadrantal made to contain them as exactly as possible. 476·687/252·458 = 1886·9 cubic inches and the cube root of the dividend gives 12·357 inches, exactly, to 1 in 20,000, the Rhineland foot as established in Prussia = 12·3564 inches. The Prussian standard of the Cologne pound (its ounce = 451·1 grains) was 1/66 of a Rhineland cubic foot of water at 65·75 F., and was fixed at 7217·9 grains. This was exactly 1/66 of 1000 Troy ounces of water at the standard of 476·38 grains. So 66 Prussian pounds were equal to 1000 Troy ounces, or to 62·5 Troy pounds at that standard. The Rhineland cubic foot had, like the English cubic foot, long been the bushel standard of North Germany. The Himt, now, or until quite recently, the unit of corn-measure in Hanover and Brunswick, contained 6·852 gallons, or 68·52 lb. of water. It is probable that the Himt, which passed to Scotland in the fifteenth century as the firlot of that time, had risen slightly, and that it was originally = 68·05 lb., the true Rhineland cubic foot of water. 3. THE PÁN OF MARSEILLES